A function f(x) satisfies (1 – xº)f"(x) – xf'(x) + f(x) = 0. (a) If n is a positive integer, what is the value of K in t

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A Function F X Satisfies 1 Xo F X Xf X F X 0 A If N Is A Positive Integer What Is The Value Of K In T 1 (73.52 KiB) Viewed 20 times

A function f(x) satisfies (1 – xº)f"(x) – xf'(x) + f(x) = 0. (a) If n is a positive integer, what is the value of K in the following (6 marks) (1 – x)f(n+2) (x) — x(2n + 1)f(n+1)(x) + K f(n)(x) = 0. — n n п Hint: (fo)" (ar) = (*) s042/() - grau/(w), where () fg() ) n-k) = n! k!(n – k)! k=0 = (b) Given that f(0) = 1 and f'(0) = 0 find the values of f"(0), f(3)(0), f(4)(0) and f( 50) Hence, determine the Maclaurin series of f(x) as far as the terms in x5. (4 marks)